Question

A racetrack is in the form of a ring whose inner and outer circumferences are 437m and 503m respectively. Find the width of the track and also its area.

Answer 1

Given below is your answer....

Answer 2

Answer:

The width of the track  is 10.5 m and the area of the track is  $4934.952 m^2$

Step-by-step explanation:

Circumference of ring = $2\pi r$

Inner circumference = 437 m

So, $437 = 2\pi r$

$437 = 2 \times \frac{22}{7} r$

$\frac{437 \times 7}{2 \times 22} = r$

$69.522 = r$

So, inner radius = 69.522 m

Outer circumference = 503 m

So, $503 = 2\pi r$

$503= 2 \times \frac{22}{7} r$

$\frac{503 \times 7}{2 \times 22} = r$

$80.022 = r$

So, Outer radius = 80.022 m

Width of track = Outer radius - Inner radius = 80.022 m- 69.522 m =10.5 m

Area of track = Outer area - inner area

                    = $\pi R^2 -\pi r^2$

                    = $\pi (R^2 -r^2)$

                    = $\frac{22}{7} \times (80.022^2 -69.522^2)$

                    = $4934.952 m^2$

Hence the width of the track  is 10.5 m and the area of the track is  $4934.952 m^2$